Nonlinear Regression Models and Applications in Agricultural Research

By Sotirios V. Archontoulis, Fernando E. Miguez. 2015

520 citations recorded by the source corpus.

Nonlinear regression models are important tools because many crop and soil processes are better represented by nonlinear than linear models. Fitting nonlinear models is not a single-step procedure but an involved process that requires careful examination of each individual step. Depending on the objective and the application domain, different priorities are set when fitting nonlinear models; these include obtaining acceptable parameter estimates and a good model fit while meeting standard assumptions of statistical models. We propose steps in fitting nonlinear models as described by a flow diagram and discuss each step separately providing examples and updates on procedures used. The following steps are considered: (i) choose candidate models, (ii) set starting values, (iii) fit models, (iv) check convergence and parameter estimates, (v) find the "best" model among competing models, (vi) check model assumptions (residual analysis), and (vii) calculate statistical descriptors and confidence intervals. The associated feedback mechanisms are also addressed (i.e., model variance homogeneity). In particular, we emphasize the first step (choose candidate models) by providing an extensive library of nonlinear functions (77 equations with the associated parameter meanings) and examples of typical applications in agriculture. We hope that this contribution will clarify some of the difficulties and confusion with the task of using nonlinear models.

Subfields: Plant Science

View Paper: https://www.semanticscholar.org/paper/df1c4c50203a99d5ce4317d099f2c334b5ca128b

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Citations in the corpus

Root to shoot and carbon to nitrogen ratios of maize and soybean crops in the US Midwest (2020, methodology): “Among many non-linear models, we used the beta function because it accounts for the biomass decline (due to leaf loss) after a certain point and because maximum biomass is one of the estimated parameters (Archontoulis and Miguez, 2015).”
Maize and soybean root front velocity and maximum depth in Iowa, USA (2018, methodology): “To identify variables that can predict root elongation we fitted nonlinear models between root elongation and explanatory variables and then a combination of statistical indexes (R(2); Archontoulis and Miguez, 2015) to identify best predictors.”
Predicting crop yields and soil‐plant nitrogen dynamics in the US Corn Belt (2020, background): “Equations can be found in Archontoulis and Miguez (2015).”